## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'bowls of instant ramen', 'granola bars', 'green beans', and 'hamburgers', which we can denote as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $7.17x_0^2 + 7.28x_1^2 + 4.4x_1x_2 + 4.41x_2x_3$.

## 3: List the constraints in symbolic notation
The constraints are:
1. $6x_0 + 15x_3 \geq 22$
2. $6x_0 + 2x_2 \geq 14$
3. $6^2x_0^2 + 16^2x_1^2 + 2^2x_2^2 \geq 21$
4. $6x_0 + 16x_1 + 15x_3 \geq 21$
5. $6^2x_0^2 + 16^2x_1^2 + 2^2x_2^2 \geq 18$
6. $6x_0 + 16x_1 + 15x_3 \geq 18$
7. $14x_0 + 16x_3 \geq 29$
8. $14x_0 + 4x_1 \geq 21$
9. $14x_0 + 4x_1 + 10x_2 \geq 23$
10. $2^2x_2^2 + 15^2x_3^2 \leq 87$
11. $6^2x_0^2 + 15^2x_3^2 \leq 74$
12. $16^2x_1^2 + 2^2x_2^2 \leq 66$
13. $6^2x_0^2 + 16^2x_1^2 \leq 95$
14. $6x_0 + 4x_1 + 2x_2 + 15x_3 \leq 95$
15. $14^2x_0^2 + 4^2x_1^2 \leq 93$
16. $14^2x_0^2 + 10^2x_2^2 \leq 110$
17. $4x_1 + 16x_3 \leq 100$
18. $4x_1 + 10x_2 \leq 139$
19. $14^2x_0^2 + 4^2x_1^2 + 10^2x_2^2 \leq 119$
20. $4^2x_1^2 + 10^2x_2^2 + 16^2x_3^2 \leq 117$
21. $14x_0 + 4x_1 + 16x_3 \leq 126$
22. $14x_0 + 4x_1 + 10x_2 + 16x_3 \leq 126$

## 4: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [
        ('x0', 'bowls of instant ramen'), 
        ('x1', 'granola bars'), 
        ('x2', 'green beans'), 
        ('x3', 'hamburgers')
    ], 
    'objective_function': '7.17*x0^2 + 7.28*x1^2 + 4.4*x1*x2 + 4.41*x2*x3', 
    'constraints': [
        '6*x0 + 15*x3 >= 22',
        '6*x0 + 2*x2 >= 14',
        '36*x0^2 + 256*x1^2 + 4*x2^2 >= 21',
        '6*x0 + 16*x1 + 15*x3 >= 21',
        '36*x0^2 + 256*x1^2 + 4*x2^2 >= 18',
        '6*x0 + 16*x1 + 15*x3 >= 18',
        '14*x0 + 16*x3 >= 29',
        '14*x0 + 4*x1 >= 21',
        '14*x0 + 4*x1 + 10*x2 >= 23',
        '4*x2^2 + 225*x3^2 <= 87',
        '36*x0^2 + 225*x3^2 <= 74',
        '256*x1^2 + 4*x2^2 <= 66',
        '36*x0^2 + 256*x1^2 <= 95',
        '6*x0 + 4*x1 + 2*x2 + 15*x3 <= 95',
        '196*x0^2 + 16*x1^2 <= 93',
        '196*x0^2 + 100*x2^2 <= 110',
        '4*x1 + 16*x3 <= 100',
        '4*x1 + 10*x2 <= 139',
        '196*x0^2 + 16*x1^2 + 100*x2^2 <= 119',
        '16*x1^2 + 100*x2^2 + 256*x3^2 <= 117',
        '14*x0 + 4*x1 + 16*x3 <= 126',
        '14*x0 + 4*x1 + 10*x2 + 16*x3 <= 126'
    ]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="x0", lb=-gurobi.GRB.INFINITY)  # bowls of instant ramen
x1 = m.addVar(name="x1", lb=-gurobi.GRB.INFINITY)  # granola bars
x2 = m.addVar(name="x2", lb=-gurobi.GRB.INFINITY)  # green beans
x3 = m.addVar(name="x3", lb=-gurobi.GRB.INFINITY)  # hamburgers

# Objective function
m.setObjective(7.17 * x0**2 + 7.28 * x1**2 + 4.4 * x1 * x2 + 4.41 * x2 * x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(6 * x0 + 15 * x3 >= 22)
m.addConstr(6 * x0 + 2 * x2 >= 14)
m.addConstr(36 * x0**2 + 256 * x1**2 + 4 * x2**2 >= 21)
m.addConstr(6 * x0 + 16 * x1 + 15 * x3 >= 21)
m.addConstr(36 * x0**2 + 256 * x1**2 + 4 * x2**2 >= 18)
m.addConstr(6 * x0 + 16 * x1 + 15 * x3 >= 18)
m.addConstr(14 * x0 + 16 * x3 >= 29)
m.addConstr(14 * x0 + 4 * x1 >= 21)
m.addConstr(14 * x0 + 4 * x1 + 10 * x2 >= 23)
m.addConstr(4 * x2**2 + 225 * x3**2 <= 87)
m.addConstr(36 * x0**2 + 225 * x3**2 <= 74)
m.addConstr(256 * x1**2 + 4 * x2**2 <= 66)
m.addConstr(36 * x0**2 + 256 * x1**2 <= 95)
m.addConstr(6 * x0 + 4 * x1 + 2 * x2 + 15 * x3 <= 95)
m.addConstr(196 * x0**2 + 16 * x1**2 <= 93)
m.addConstr(196 * x0**2 + 100 * x2**2 <= 110)
m.addConstr(4 * x1 + 16 * x3 <= 100)
m.addConstr(4 * x1 + 10 * x2 <= 139)
m.addConstr(196 * x0**2 + 16 * x1**2 + 100 * x2**2 <= 119)
m.addConstr(16 * x1**2 + 100 * x2**2 + 256 * x3**2 <= 117)
m.addConstr(14 * x0 + 4 * x1 + 16 * x3 <= 126)
m.addConstr(14 * x0 + 4 * x1 + 10 * x2 + 16 * x3 <= 126)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```